Systolic ratio, index of closed orbits and convexity for tight contact forms on the three-sphere
Abstract
We construct a dynamically convex contact form on the three-sphere whose systolic ratio is arbitrarily close to 2. This example is related to a conjecture of Viterbo, whose validity would imply that the systolic ratio of a convex contact form does not exceed 1. We also construct a sequence of tight contact forms $\alpha_n$, $n\geq 2$, with systolic ratio arbitrarily close to $n$ and suitable bounds on the mean rotation number of all the closed orbits of the induced Reeb flow.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2017
- DOI:
- 10.48550/arXiv.1710.06193
- arXiv:
- arXiv:1710.06193
- Bibcode:
- 2017arXiv171006193A
- Keywords:
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- Mathematics - Symplectic Geometry
- E-Print:
- 44 pages